A151389 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 1), (0, -1), (1, 1)}.

1, 0, 2, 2, 10, 22, 82, 220, 808, 2356, 8656, 26654, 98102, 312984, 1156032, 3782616, 14015132, 46756952, 173680748, 588380312, 2190211648, 7512444672, 28014835088, 97081546938, 362582983586, 1267349177760, 4739583478208, 16688334026768, 62482287911704, 221396939695828, 829766494964876, 2956346830527760

Offset

0,3

Links

Table of n, a(n) for n=0..31.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A151456 A336490 A230893 * A151428 A341680 A213338

Adjacent sequences: A151386 A151387 A151388 * A151390 A151391 A151392

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved